Blow‐up profiles of solutions for the exponential reaction‐diffusion equation |
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| Authors: | A Pulkkinen |
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| Institution: | Aalto University, Institute of Mathematics, , P.O. Box 11100, FI‐00076 Aalto, Finland |
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| Abstract: | We consider the blow‐up of solutions for a semilinear reaction‐diffusion equation with exponential reaction term. It is known that certain solutions that can be continued beyond the blow‐up time possess a non‐constant self‐similar blow‐up profile. Our aim is to find the final time blow‐up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach works also for the power nonlinearity. Copyright © 2011 John Wiley & Sons, Ltd. |
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| Keywords: | nonlinear heat equation exponential reaction blow‐up blow‐up profile |
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